{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Protein-ligand binding process analysis with MSM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "In this tutorial, we demonstrate how to use the HTMD code for analysing a protein-ligand binding process.\n",
    "\n",
    "To analyze, one needs MD trajectories first, which can be generated with HTMD. Here, we already provide the trajectories (data) to analyze. You can download the data from [here](http://pub.htmd.org/tutorials/ligand-binding-analysis/datasets.tar.gz). (**Warning: 3GB filesize**)\n",
    "\n",
    "Alternatively, you can download the dataset using `wget`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "assert os.system('wget -rcN -np -nH -q --cut-dirs=2 -R index.html* http://pub.htmd.org/tutorials/ligand-binding-analysis/datasets/') == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Getting started"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "First we import the modules we are going to need for the tutorial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "\n",
      "Please cite HTMD: Doerr et al.(2016)JCTC,12,1845. \n",
      "https://dx.doi.org/10.1021/acs.jctc.6b00049\n",
      "Documentation: http://software.acellera.com/\n",
      "To update: conda update htmd -c acellera -c psi4\n",
      "\n",
      "You are on the latest HTMD version (unpackaged : /home/joao/maindisk/software/repos/Acellera/htmd/htmd).\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from htmd.ui import *\n",
    "config(viewer='webgl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Creating a simulation list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the purposes of an analysis, full atom information is required by HTMD. Therefore each simulation trajectory has to be associated with a corresponding PDB file. Additionally, if you plan to run adaptive, each trajectory needs to be associated with an input directory which contains the files used to run the simulations. The `simlist` function allows us to make these associations\n",
    "\n",
    "```python\n",
    "sims = simlist(glob('data/*/'), glob('input/*/structure.pdb'), glob('input/*/'))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Filtering trajectories"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Typically waters are removed from the trajectories as they are not used in the analysis and it helps speed up further calculations. These filtered trajectories are written into a new directory. The advantage of filtering is that if your input structures only differ in the number of water molecules, you can produce a single unique pdb file for all simulations once you remove the waters, which will speed up calculations. This step is not necessary for the analysis and you can skip it if you don't mind the slowdown in calculations. In that case replace in the following commands the fsims variable with sims.\n",
    "```python\n",
    "fsims = simfilter(sims, './filtered/', filtersel='not water')\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In this tutorial, in order for the trajectories to be downloaded in a timely manner, we provide only the filtered trajectories, which are stored in three separate dataset folders. Therefore we will skip the above two commands and construct the simulation list directly from the filtered trajectories:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Creating simlist: 100%|██████████| 314/314 [00:00<00:00, 2849.42it/s]\n",
      "Creating simlist: 100%|██████████| 309/309 [00:00<00:00, 2941.33it/s]\n",
      "Creating simlist: 100%|██████████| 230/230 [00:00<00:00, 2940.73it/s]\n"
     ]
    }
   ],
   "source": [
    "sets = glob('datasets/*/')\n",
    "sims = []\n",
    "for s in sets:\n",
    "    fsims = simlist(glob(s + '/filtered/*/'), 'datasets/1/filtered/filtered.pdb')\n",
    "    sims = simmerge(sims, fsims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Calculating metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To build a Markov state model we need to project the atom coordinates onto a lower dimensional space which can be used for clustering the conformations into a set of states. For protein systems we typically use the binary contact map between the carbon alpha atoms of the protein. This will calculate contacts between all carbon-alpha atoms. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Projecting trajectories: 100%|██████████| 852/852 [00:15<00:00, 55.03it/s]\n",
      "2018-03-19 23:17:49,465 - htmd.projections.metric - INFO - Frame step 9.999999974752427e-07ns was read from the trajectories. If it looks wrong, redefine it by manually setting the MetricData.fstep property.\n"
     ]
    }
   ],
   "source": [
    "metr = Metric(sims)\n",
    "metr.set(MetricDistance('protein and name CA', 'resname MOL and noh', metric='contacts'))\n",
    "data = metr.project()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we also provide the frame-step in nanoseconds i.e. the time that passes between two consecutive frames in a trajectory. This should be automatically read from the trajectories, but some simulation software does not contain the correct fstep in the trajectories, so it can be useful to manually define it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.fstep = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Removing trajectories"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes the set of trajectories can contain trajectories of incorrect length. These are typically corrupted trajectories and are removed.\n",
    "\n",
    "The `plotTrajSizes` method plots all trajectory lengths, sorted:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5PLA+nXObpK0UY1Y/vbPnNzOznddtgpD01z3sFxHxvxodPCJ+AxwlaSRwK/CGXLXaKXvYVh/XbGA2wKRJkxqFYGZmO6mnR0wvZiYo2grO781JIuJZYCkwBRgpqZaYJgAb0nInMBEgbd8feCZzrHkR0RERHW1tbb0Jw8zMeqHbBBERX69NwDxgT+AM4Hrg0EYHltSW7hyQtCdwPLAauAs4OVWbCSxMy4vSOmn7jyOiTGO4mZlVoMc2CEmjKd46+ghFA/LREbGl5LEPBBakdojdgBsj4geSHgGul/S3wP0Uo9WR5v8kaS3FncOpvb4aMzPrNz21QXwN+ADF3cMf1r2RVEpErALelCl/nMyHdhHxMnBKb85hZmbV6akN4lzgIOCLwAZJz6XpeUnPNSc8MzNrlW7vICKi119Zm5nZ4OEkYGZmWU4QZmaW5QRhZmZZThBmZpblBGFmZllOEGZmluUEYWZmWU4QZmaW5QRhZmZZThBmZpblBGFmZllOEGZmluUEYWZmWZUlCEkTJd0labWkhyWdncpHS1osaU2aj0rlknSZpLWSVkk6uqrYzMyssSrvILYB50bEGyjGoj5T0pHAXGBJREwGlqR1gBOAyWmaDVxRYWxmZtZAZQkiIjZGxIq0/DzFeNTjgekUw5eS5jPS8nTgmijcA4yUdGBV8ZmZWc+a0gYhqZ1i+NF7gXERsRGKJAKMTdXGA+vrdutMZWZm1gKVJwhJ+wDfA+ZERE9DlSpTFpnjzZa0TNKyzZs391eYZmbWRaUJQtLuFMnh2oi4JRU/VXt0lOabUnknMLFu9wnAhq7HjIh5EdERER1tbW3VBW9mNsRV+RaTgKuA1RHxjbpNi4CZaXkmsLCu/LT0NtMUYGvtUZSZmTXf8AqPfRzwMeBBSStT2eeBC4EbJc0CngROSdtuB04E1gIvAWdUGJuZmTVQWYKIiJ+Sb1cAmJapH8CZVcVjZma94y+pzcwsywnCzMyynCDMzCzLCcLMzLKcIMzMLMsJwszMspwgzMwsywnCzMyynCDMzCzLCcLMzLKcIMzMLMsJwszMspwgzMwsywnCzMyynCDMzCzLCcLMzLKqHHL0u5I2SXqormy0pMWS1qT5qFQuSZdJWitplaSjq4rLzMzKqfIOYj7w7i5lc4ElETEZWJLWAU4AJqdpNnBFhXGZmVkJlSWIiPgJ8EyX4unAgrS8AJhRV35NFO4BRko6sKrYzMyssWa3QYyLiI0AaT42lY8H1tfV60xlO5A0W9IyScs2b95cabBmZkPZQGmkVqYschUjYl5EdERER1tbW8VhmZkNXc1OEE/VHh2l+aZU3glMrKs3AdjQ5NjMzKxOsxPEImBmWp4JLKwrPy29zTQF2Fp7FGVmZq0xvKoDS7oOeAcwRlIncAFwIXCjpFnAk8ApqfrtwInAWuAl4Iyq4jIzs3IqSxAR8eFuNk3L1A3gzKpiMTOz3hsojdRmZjbAOEGYmVmWE4SZmWU5QZiZWZYThJmZZTlBmJlZlhOEmZllOUGYmVmWE4SZmWU5QZiZWZYThJmZZTlBmJlZlhOEmZllOUGYmVmWE4SZmWUNqAQh6d2SHpO0VtLcVsdjZjaUDZgEIWkY8C3gBOBI4MOSjmxtVGZmQ9eASRDAscDaiHg8Il4FrgemtzgmM7MhayAliPHA+rr1zlRmZmYtUNmY1DtBmbLYoZI0G5idVl+Q9FiD444Bnu5jbLsiX/fQMlSvG4boteuiPl33wWUqDaQE0QlMrFufAGzoWiki5gHzyh5U0rKI6Oh7eLsWX/fQMlSvG4butTfjugfSI6b7gMmSDpE0AjgVWNTimMzMhqwBcwcREdskfRL4V2AY8N2IeLjFYZmZDVkDJkEARMTtwO39fNjSj6MGGV/30DJUrxuG7rVXft2K2KEd2MzMbEC1QZiZ2QAyqBKEpO9K2iTpobqy0ZIWS1qT5qNaGWMVurnur0l6VNIqSbdKGtnKGKuQu+66bedJCkljWhFblbq7bklnpa5qHpb01VbFV5Vu/js/StI9klZKWibp2FbGWAVJEyXdJWl1+rc9O5VX/ts2qBIEMB94d5eyucCSiJgMLEnrg818drzuxcAfRMQfAf8P+Fyzg2qC+ex43UiaCPwJ8GSzA2qS+XS5bknvpOh54I8i4veBi1sQV9Xms+O/91eBr0TEUcBfp/XBZhtwbkS8AZgCnJm6Iar8t21QJYiI+AnwTJfi6cCCtLwAmNHUoJogd90RcWdEbEur91B8VzKodPPvDXAJ8FkyH1oOBt1c9yeACyPilVRnU9MDq1g31x3Afml5fzLfTu3qImJjRKxIy88Dqyl6maj8t21QJYhujIuIjVD8oYGxLY6nFf4H8KNWB9EMkk4Cfh4RD7Q6liY7AnibpHsl3S3pj1sdUJPMAb4maT3FXdNgvFP+LUntwJuAe2nCb9tQSBBDmqQvUNyiXtvqWKomaS/gCxSPGoaa4cAoikcQnwFulJTrvmaw+QTw6YiYCHwauKrF8VRG0j7A94A5EfFcM845FBLEU5IOBEjzQXfr3R1JM4H3Ah+JofE+82HAIcADktZRPFZbIem/tTSq5ugEbonCz4DXKPooGuxmArek5ZsoeoUedCTtTpEcro2I2vVW/ts2FBLEIor/iEjzhS2MpWkkvRs4HzgpIl5qdTzNEBEPRsTYiGiPiHaKH82jI+IXLQ6tGb4PTAWQdAQwgqHRgd0G4L+n5anAmhbGUol0J3gVsDoivlG3qfrftogYNBNwHbAR+DXFj8Ms4ACKFv41aT661XE26brXUnSfvjJN32l1nM247i7b1wFjWh1nk/69RwD/DDwErACmtjrOJl33W4HlwAMUz+WPaXWcFVz3Wyka41fV/e/5xGb8tvlLajMzyxoKj5jMzGwnOEGYmVmWE4SZmWU5QZiZWZYThJmZZTlBWJ9IeqHi458u6aC69XV96aFV0nWph9tPdymfkTpA6+3xTpK0U52kSfr8Tu53e3/0zitpjqTT0vLfSDq+r8fs4VwXS5pa1fGtGn7N1fpE0gsRsU+Fx18KnBcRy9L6OqAjInr9EVj6ovreiDg4s20+8IOIuDmzbXhs7/iw3/T2b5c+mFJEvNYP5x5O8b3E0VVcW+Z8BwP/GBHvqvpc1n98B2H9TlKbpO9Jui9Nx6XyL6c+/ZdKelzSp+r2+VIav2Jx+n/550k6GegArk39/e+Zqp8laYWkByW9PnP+PSRdnbbfn7rCBrgTGJuO9ba6+m8BTqLo9G2lpMNSjP9b0t3A2ZLelzrCu1/S/5E0Lu17uqS/b3Dd+9TFs0rSByVdCOyZzndtqneOpIfSNCeVtadxAL5N8YM+sf4uStJHJf0sHecfJA1L0/x0nAe73i0lU4EVteSQ6p+cltdJ+kqDv/Hpkm6RdIeK8Qi+msqz546IJ4ADNDS6PRk8Wv2VoKddewJeyJT9C/DWtDyJoosAgC8D/wG8jqKfoF8Cu1MkgZXAnsC+FF+Gnpf2WUpxx1A79jrgrLT8V8CVmfOfC1ydll9PMS7EHkA78FA31zEfOLlufSnw7br1UWy/4/6fwNfT8unA3ze47ouAb9Yfq+vfDjgGeBDYG9gHeJii1852in6VpnT5G4wB3gDcBuyeyr8NnJaOtbiu/sjM9X6l9nfsev0l/8anA49TdLG9B/AEMLGncwP/CHyw1f/Neio/Dces/x0PHKntnYnuJ2nftPzDKMYseEXSJmAcRVcCCyPiVwCSbmtw/FpnZcuBD2S2vxW4HCAiHpX0BEV32L3tAfOGuuUJwA0qOkUbAfxXpn531308cGqtMCK2dBPzrRHxIoCkW4C3UfS380RE3JPZZxrFD/J96Zx7UnTYdhtwqKTLgR9S3Dl1dSDFuALdafQ3hmKwmq0p3keAgykSW3fn3gQctMNRbMBygrAq7Aa8ufaDX5N+xF6pK/oNxX+Dve2WunaM2v5d9Vc31y/WLV8OfCMiFkl6B8XdUFfdXbdoPHhRTzG/2E25gAURscMYCJLeCPwpcCbwIYoxQer9iuL/+Xen0d+4vs5v60XElh7OvUc6r+0i3AZhVbgT+GRtRdJRDer/FHhfajvYB3hP3bbnKR479cZPgI+kcx9B8bjnsQb7NDrP/sDP0/LMbup0d91dy2tjB/9aRTfOtZhnSNpL0t7A+4F/axDzEuBkSWPTcUdLOji1T+wWEd8DvgQcndl3NXB4g+P3WoNzH0HRmaDtIpwgrK/2ktRZN50DfAroSA2yjwAf7+kAEXEfxaOUBygebSwDtqbN84HvdGmkbuTbwDBJD1I8Jjo9PdbqyfXAZ1Ij9GGZ7V8GbpL0b+zYjXbt7qC76/5bYFRquH0AqDWazwNWSbo2iiEl5wM/o+iV9MqIuL+ngCPiEeCLwJ2SVlGMQ34gxXCUSyWtTMfMjbL2I+DtPR1/J2XPnRLh4RT/traL8GuuNiBI2iciXlAxKtxPgNnpR3NAk3QusF9EXNDqWHpL0q3AZyOi8jEUJL2f4pXaL1V9Lus/boOwgWKeig/V9qB4rr4rJIePU7zN010j7kA3l+KOoxmD7AwHvt6E81g/8h2EmZlluQ3CzMyynCDMzCzLCcLMzLKcIMzMLMsJwszMspwgzMws6/8D3YFcJQ0SLHMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plotTrajSizes()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The `dropTraj` method has multiple options for removing simulations from the dataset. Here, we use it to remove all trajectories whose length is not equal to the mode length:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2018-03-19 23:18:00,335 - htmd.metricdata - INFO - Dropped 2 trajectories from 852 resulting in 850\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([496, 562])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.dropTraj()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## TICA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TICA is a method that can be used to improve the clustering of the conformations. This is done by projecting the data onto a lower-dimensional space which separates well the metastable minima and places clusters on the transition regions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/joao/maindisk/SANDBOX/miniconda3/miniconda3/lib/python3.6/site-packages/pyemma/__init__.py:91: UserWarning: You are not using the latest release of PyEMMA. Latest is 2.5.1, you have 2.4.\n",
      "  .format(latest=latest, current=current), category=UserWarning)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a6c1f523f10443929feb49b32a00ed77",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e9bf593b622e4d5cb6778e6c8979d903",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tica = TICA(data, 2, units='ns')\n",
    "dataTica = tica.project(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bootstrapping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "If we want to bootstrap our calculations we can at this point drop a random 20% of the trajectories and do the rest of the analysis multiple times to see if the results are consistent. Alternatively we can keep on using dataTica in the following commands. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataBoot = dataTica.bootstrap(0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Clustering conformations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Once we have cleaned the dataset we proceed to cluster the conformations.\n",
    "\n",
    "Here we use the mini-batch kmeans clustering algorithm to produce 1000 clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataBoot.cluster(MiniBatchKMeans(n_clusters=1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Building the Markov model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After clustering it is time to build the Markov model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Model(dataBoot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before constructing the Markov model, we need to choose the lag-time at which it will be built. The lag-time is typically chosen by looking at the implied timescale (ITS) plot and selecting a lag-time at which the top timescales start converging. By constructing Markov models at various lag times HTMD creates a plot which shows the slowest implied timescales of each Markov model at various lag times. If a model is Markovian at a specific lag time, the implied timescales should stay unchanged for any higher lag times. Therefore, given an implied timescales plot, the user can monitor the convergence and choose the lag time at which to construct his Markov model, typically the Markov time which is the shortest lag time at which the timescales converge. Too large lag times can reduce the temporal resolution of the Markov model and can create more statistical uncertainty due to fewer transition counts and thus instability in the implied timescales. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "99cb74772fe24bb998ad18d5a9dbb987",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plotTimescales()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After seeing the ITS plot we decided on a lag-time of 50 frames (5ns). Additionally the ITS plot showed us that there is a separation between 4 slow timescales and the rest of the timescales which are fast. Therefore we choose to lump our microstates together into 5 macrostates. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2018-03-19 23:38:49,319 - htmd.model - INFO - 100.0% of the data was used\n",
      "2018-03-19 23:38:49,359 - htmd.model - INFO - Number of trajectories that visited each macrostate:\n",
      "2018-03-19 23:38:49,360 - htmd.model - INFO - [156 101 117 363 226]\n"
     ]
    }
   ],
   "source": [
    "model.markovModel(5, 5, units='ns')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Once we have a Markov model we can plot the free energy surface by projecting it on any of our projected coordinates. For example to plot it on the first two TICA coordinates we call it like this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/joao/maindisk/software/repos/Acellera/htmd/htmd/metricdata.py:786: MatplotlibDeprecationWarning: The griddata function was deprecated in version 2.2.\n",
      "  zi = griddata(x, y, z, xi, yi, interp='linear')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plotFES(0, 1, temperature=298)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can also plot the micro and macrostates on top of the FES by setting `states=True`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/joao/maindisk/software/repos/Acellera/htmd/htmd/metricdata.py:786: MatplotlibDeprecationWarning: The griddata function was deprecated in version 2.2.\n",
      "  zi = griddata(x, y, z, xi, yi, interp='linear')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plotFES(0, 1, temperature=298, states=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Visualizing the states"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "To see what the states look like we can use the `viewStates` method. We load the macrostates and add a ligand representation using the ligand atomselection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Getting state Molecules: 100%|██████████| 5/5 [00:06<00:00,  1.38s/it]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e566fcf695154d64803dcf349a595b41",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "caafd43aecc441449666dce2fb6b6e4f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.viewStates(ligand='resname MOL and noh')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Calculating the kinetics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the major advantages of Markov state models is that they can provide quantitative results about the kinetics between states.\n",
    "\n",
    "Provide the `Kinetics` class with the system temperature and ligand concentration. It automatically then calculates the source and sink states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2018-03-19 23:39:40,195 - htmd.kinetics - INFO - Detecting source state...\n",
      "2018-03-19 23:39:41,168 - htmd.kinetics - INFO - Guessing the source state as the state with minimum contacts.\n",
      "2018-03-19 23:39:41,170 - htmd.kinetics - INFO - Source macro = 3\n",
      "2018-03-19 23:39:41,171 - htmd.kinetics - INFO - Detecting sink state...\n",
      "2018-03-19 23:39:41,210 - htmd.kinetics - INFO - Sink macro = 4\n"
     ]
    }
   ],
   "source": [
    "kin = Kinetics(model, temperature=298, concentration=0.0037)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To see the rates between the source and sink states we use the getRates method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2018-03-19 23:39:51,759 - htmd.kinetics - INFO - Calculating rates between source: [3] and sink: [4] states.\n",
      "2018-03-19 23:39:52,074 - htmd.kinetics - INFO - Concentration correction of -3.32 kcal/mol.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mfpton = 9.84E+02 (ns)\n",
      "mfptoff = 4.35E+03 (ns)\n",
      "kon = 2.75E+08 (1/M 1/s)\n",
      "koff = 2.30E+05 (1/s)\n",
      "koff/kon = 8.37E-04 (M)\n",
      "kdeq = 6.26E-04 (M)\n",
      "g0eq = -4.37 (kcal/M)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "r = kin.getRates()\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To plot the free energies and mean first passage times of all state relative to the source state, use the `plotRates` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kin.plotRates()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To visualize the kinetic flux pathways between the source and sink states, use the `plotFluxPathways` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/joao/maindisk/SANDBOX/miniconda3/miniconda3/lib/python3.6/site-packages/pyemma/plots/networks.py:544: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if state_labels == 'auto':\n",
      "/home/joao/maindisk/SANDBOX/miniconda3/miniconda3/lib/python3.6/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
      "  \"matplotlib is currently using a non-GUI backend, \"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Path flux\t\t%path\t%of total\tpath\n",
      "1.3443951293549833e-05\t66.3%\t66.3%\t\t[3 4]\n",
      "6.107254749717703e-06\t30.1%\t96.4%\t\t[3 2 4]\n",
      "7.357397291918617e-07\t3.6%\t100.0%\t\t[3 1 4]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kin.plotFluxPathways()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And this concludes the ligand binding tutorial."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
